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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "过拟合和欠拟合\n",
    "'''\n",
    "%matplotlib inline\n",
    "import d2lzh as d2l\n",
    "from mxnet import autograd, gluon, nd\n",
    "from mxnet.gluon import data as gdata, loss as gloss, nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "生成数据集\n",
    "'''\n",
    "n_train, n_test, true_w, true_b = 100, 100, [1.2, -3.4, 5.6], 5\n",
    "features = nd.random.normal(shape=(n_train+n_test, 1))\n",
    "poly_features = nd.concat(features, nd.power(features, 2), nd.power(features, 3))\n",
    "labels = (true_w[0] * poly_features[:,0] + true_w[1] * poly_features[:,1] + true_w[2] * poly_features[:,2] + true_b)\n",
    "labels += nd.random.normal(scale=0.01, shape=labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(\n",
       " [[1.1630785]\n",
       "  [0.4838046]]\n",
       " <NDArray 2x1 @cpu(0)>,\n",
       " \n",
       " [[1.1630785  1.3527517  1.5733565 ]\n",
       "  [0.4838046  0.2340669  0.11324265]]\n",
       " <NDArray 2x3 @cpu(0)>,\n",
       " \n",
       " [10.599886   5.4300165]\n",
       " <NDArray 2 @cpu(0)>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features[:2], poly_features[:2], labels[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "定义、训练和测试模型\n",
    "'''\n",
    "def semilogy(x_vals, y_vals, x_label, y_label, x2_vals=None, y2_vals=None,\n",
    "            legend=None, figsize=(3.5, 2.5)):\n",
    "    d2l.set_figsize(figsize)\n",
    "    d2l.plt.xlabel(x_label)\n",
    "    d2l.plt.ylabel(y_label)\n",
    "    d2l.plt.semilogy(x_vals, y_vals)\n",
    "    if x2_vals and y2_vals:\n",
    "        d2l.plt.semilogy(x2_vals, y2_vals, linestyle=':')\n",
    "        d2l.plt.legend(legend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs, loss = 100, gloss.L2Loss()\n",
    "\n",
    "def fit_and_plot(train_features, test_features, train_labels, test_labels):\n",
    "    net = nn.Sequential()\n",
    "    net.add(nn.Dense(1))\n",
    "    net.initialize()\n",
    "    batch_size = min(10, train_labels.shape[0])\n",
    "    train_iter = gdata.DataLoader(gdata.ArrayDataset(\n",
    "            train_features, train_labels), batch_size, shuffle=True)\n",
    "    trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.01})\n",
    "    train_ls, test_ls = [], []\n",
    "    for _ in range(num_epochs):\n",
    "        for X, y in train_iter:\n",
    "            with autograd.record():\n",
    "                l = loss(net(X), y)\n",
    "            l.backward()\n",
    "            trainer.step(batch_size)\n",
    "        train_ls.append(loss(net(train_features),train_labels).mean().asscalar())\n",
    "        test_ls.append(loss(net(test_features), test_labels).mean().asscalar())\n",
    "    print('final epoch: train loss', train_ls[-1], 'test loss', test_ls[-1])\n",
    "    semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'loss',\n",
    "            range(1, num_epochs + 1), test_ls, ['train', 'test'])\n",
    "    print('weight:', net[0].weight.data().asnumpy(),\n",
    "         '\\nbias:', net[0].bias.data().asnumpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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      "weight: [[ 1.163691  -3.3902817  5.6089597]] \n",
      "bias: [4.97719]\n"
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   "source": [
    "'''\n",
    "线性函数拟合非线性函数（欠拟合）\n",
    "'''\n",
    "fit_and_plot(features[:n_train,:], features[n_train:,:], labels[:n_train], \n",
    "             labels[n_train:])"
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   "cell_type": "code",
   "execution_count": 9,
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   ],
   "source": [
    "'''\n",
    "训练样本不足（过拟合）\n",
    "'''\n",
    "fit_and_plot(poly_features[0:2, :], poly_features[n_train:, :], labels[0:2], \n",
    "             labels[n_train:])"
   ]
  }
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